Main Article Content

Abstract

We introduce a new extension of the reciprocal Exponential distribution for modeling the extreme values. We used the Morgenstern family and the clayton copula for deriving many bivariate and multivariate extensions of the new model. Some of its properties are derived. We assessed the performance of the maximum likelihood estimators (MLEs) via a graphical simulation study. The assessment was based on the sample size. The new reciprocal model is employed for modeling the skewed and the symmetric real data sets. The new reciprocal model is better than some other important competitive models in statistical modeling.

Keywords

Reciprocal Exponential Distribution Morgenstern Family Moments Clayton Copula Estimation Simulations Odd Log-Logistic Family

Article Details

How to Cite
Mansour, M. M., Butt, N. S., Yousof, H., Ansari, S. I., & Ibrahim, M. (2020). A Generalization of Reciprocal Exponential Model: Clayton Copula, Statistical Properties and Modeling Skewed and Symmetric Real Data Sets: A Generalization of Reciprocal Exponential Model. Pakistan Journal of Statistics and Operation Research, 16(2), 373-386. https://doi.org/10.18187/pjsor.v16i2.3298

References

  1. Aarset, M. V. (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36(1), 106-108.
  2. Al-Babtain, A. A. Elbatal, I. and Yousof, H. M. (2020a). A new three parameter Fréchet model with mathematical properties and applications. Journal of Taibah University for Science, 14(1), 265–278.
  3. Al-Babtain, A. A. Elbatal, I. and Yousof, H. M. (2020b). A new flexible three-parameter model: properties, Clayton Copula, and modeling real data, Symmetry, 12, 1-17. doi:10.3390/sym12030440
  4. Basikhasteh, M., Lak, F., Alizadeh, M. and Yousof, H. M. (2018). The Odd Log-Logistic Generalized Half-Normal Lifetime Poisson Model, Pak. J. Stat. Oper. Res. 14(3), 111-128.
  5. Brito, E., Cordeiro, G. M., Yousof, H. M., Alizadeh, M. and Silva, G. O. (2017). Topp-Leone Odd Log-Logistic Family of Distributions, Journal of Statistical Computation and Simulation, 87(15), 3040-3058.
  6. Chakraborty, S., Handique, L., Altun, E. and Yousof, H. M. (2018). A new statistical model for extreme values: mathematical properties and applications. International Journal of Open Problems in Computer Science and Mathematics, 12(1), 1-18.
  7. Cordeiro, G. M., Alizadeh, M. M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E. (2016). The generalized odd log-logistic family of distributions: properties, regression models and applications, Journal of Statistical Computation and Simulation, 87(5), 908-932.
  8. Cordeiro, G. M., Yousof, H. M., Ramires, T. G. and Ortega, E. M. M. (2018). The Burr XII system of densities: properties, regression model and applications. Journal of Statistical Computation and Simulation, 88(3), 432-456.
  9. Elbiely, M. M. and Yousof, H. M. (2018). A new extension of the Lomax distribution and its applications, Journal of Statistics and Applications, 2(1), 18-34.
  10. Elbiely, M. M. and Yousof, H. M. (2019). A new inverse Weibull distribution: properties and applications. Journal of Mathematics and Statistics, 15(1), 30-43.
  11. Fréchet, M. (1927). Sur la loi de probabilité de lécart maximum. Ann. de la Soc. polonaisede Math, 6, 93--116.
  12. Gleaton, J. U. and Lynch, J. D. (2006). Properties of generalized loglogistic families of lifetime distributions. Journal of Probability and Statistical Science, 4, 51-64.
  13. Gad, A. M., Hamedani, G. G., Salehabadi, S. M. and Yousof, H. M. (2019). The Burr XII-Burr XII distribution: mathematical properties and characterizations. Pakistan Journal of Statistics, 35(3), 229-248.
  14. Goual, H. and Yousof, H. M. (2019). Validation of Burr XII inverse Rayleigh model via a modified chi-squared goodness-of-fit test. Journal of Applied Statistics, 47(1), 1-32.
  15. Gupta, R. C. and Gupta, R. D. (2007). Proportional reversed hazard rate model and its applications. J. Statist Plan Inference.137, 3525--3536.
  16. Hamedani G. G., Altun, E, Korkmaz, M. C., Yousof, H. M. and Butt, N. S. (2018). A new extended G family of continuous distributions with mathematical properties, characterizations and regression modeling. Pak. J. Stat. Oper. Res., 14 (3), 737-758.
  17. Hamedani G. G. Rasekhi, M., Najibi, S. M., Yousof, H. M. and Alizadeh, M., (2019). Type II general exponential class of distributions. Pak. J. Stat. Oper. Res., XV(2), 503-523.
  18. Hamedani G. G. Yousof, H. M., Rasekhi, M., Alizadeh, M. and Najibi, S. M. (2017). Type I general exponential class of distributions. Pak. J. Stat. Oper. Res., XIV(1), 39-55.
  19. Ibrahim, M. (2019). A new extended Fréchet distribution: properties and estimation. Pak. J. Stat. Oper. Res.,15 (3), 773-796.
  20. Ibrahim, M. (2020a). The compound Poisson Rayleigh Burr XII distribution: properties and applications. Journal of Applied Probability and Statistics, 15(1), 73-97.
  21. Ibrahim, M. (2020b). The generalized odd Log-logistic Nadarajah Haghighi distribution: statistical properties and different methods of estimation. Journal of Applied Probability and Statistics, forthcoming.
  22. Ibrahim, M., Altun, E. and Yousof, H. M. (2020). A new distribution for modeling lifetime data with different methods of estimation and censored regression modeling. Statistics, Optimization and Information Computing, 8, 610–630.
  23. Ibrahim, M. and Yousof, H. M. (2020). A new generalized Lomax model: statistical properties and applications, Journal of Data Science, 18(1), 190 – 217.
  24. Ibrahim, M., Yadav, A. S. Yousof, H. M., Goual, H. and Hamedani, G. G. (2019). A new extension of Lindley distribution: modified validation test, characterizations and different methods of estimation, Communications for Statistical Applications and Methods, 26(5), 473–495.
  25. Khalil, M. G., Hamedani G. G. and Yousof, H. M. (2019). The Burr X exponentiated Weibull model: characterizations, mathematical properties and applications to failure and survival times data. Pak. J. Stat. Oper. Res., XV(1), 141-160.
  26. Korkmaz, M. C., Alizadeh, M., Yousof, H. M. and Butt, N. S. (2018). The generalized odd Weibull generated family of distributions: statistical properties and applications. Pak. J. Stat. Oper. Res., 14 (3), 541-556.
  27. Korkmaz, M. C., Altun, E., Yousof, H. M. and Hamedani G. G. (2019). The Odd Power Lindley Generator of Probability Distributions: Properties, Characterizations and Regression Modeling, International Journal of Statistics and Probability, 8(2). 70-89.
  28. Korkmaz, M. C. Yousof, H. M. and Ali, M. M. (2017). Some Theoretical and Computational Aspects of the Odd Lindley Fréchet Distribution, Journal of Statisticians: Statistics and Actuarial Sciences, 2, 129-140.
  29. Mansour, M., Yousof, H. M., Shehata, W. A. M. and Ibrahim, M. (2020). A new two parameter Burr XII distribution: properties, copula, different estimation methods and modeling acute bone cancer data, Journal of Nonlinear Science and Applications, 13, 223–238.
  30. Nichols, M. D, Padgett, W. J. (2006). A Bootstrap control chart for Weibull percentiles. Quality and Reliability Engineering International, 22, 141-151.
  31. Smith, R. L. and Naylor, J. C. (1987). A comparison of maximum likelihood and bayesian estimators for the three-parameter Weibull distribution. Applied Statistics, 36, 358-369.
  32. Yousof, H. M., Afify, A. Z., Alizadeh, M., Butt, N. S., Hamedani, G. G. and Ali, M. M. (2015). The transmuted exponentiated generalized-G family of distributions. Pak. J. Stat. Oper. Res., 11, 441-464.
  33. Yousof, H. M., Afify, A. Z., Ebraheim, A. N., Hamedani, G. G. and Butt, N. S. (2016). On six-parameter Fréchet distribution: properties and applications, Pak. J. Stat. Oper. Res., 12, 281-299.
  34. Yousof, H. M., Alizadeh, M., Jahanshahi and, S. M. A., Ramires, T. G., Ghosh, I. and Hamedani G. G. (2017). The transmuted Topp-Leone G family of distributions: theory, characterizations and applications, Journal of Data Science. 15, 723-740.
  35. Yousof, H. M., Altun, E. and Hamedani, G. G. (2018 a). A new extension of Frechet distribution with regression models, residual analysis and characterizations. Journal of Data Science, 16(4), 743-770.
  36. Yousof, H. M., Jahanshahi, S. M., Ramires, T. G Aryal, G. R. and Hamedani G. G. (2018 b). A new distribution for extreme values: regression model, characterizations and applications. Journal of Data Science, 16(4), 677-706.